I cannot say why they changed their name but can state
LINK to 1901 census where shown as CONE; dated March 31st 1901
Their child Theresa was registered as REDDINGTON on April 8th 1901!
LINKMost of their children seem to have been born at Tea Lane which would imply perhaps some subterfuge with the constable who was filling in the census return!
What I did notice, although bearing in mind COEN is a common name in Galway,
one of the sponsors at Patrick's baptism in 1887 was a Thomas COEN
This is not yet freely online